Only female Dhampir give birth to Dhampir, and they can only do so with a Moroi. Dhampir cannot reproduce together. 

Most Dhampir just use their mother's last name, since most Moroi men don't marry Dhampir women, but since we aren't really following the books story line,  then sure you can give your Dhampir a Royal Moroi last name. 

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On another note, where would you guys like the schools academy located?